# Thread: how would I apply Bayes theorem?

1. ## how would I apply Bayes theorem?

Machines I and II respectively produce 70% and 30% of a factory’s output. Machine I produces 2% defectives and machine II produces 3% defectives. If an item is not defective, what is the chance it was produced by machine I?

Which event would be A and which one B?

3. I will let A stand for machine one and B for machine 2.

You have $P(A)=.7$ and $P(B)=.3$ as the partition.

Next you have $P(D|A)=.02$ and $P(D|B)=.03$ where D stands for defective.

So the probability of defective is

$P(D)=P(DA)+P(DB)= P(D|A)P(A)+P(D|B)P(B)$

$=(.02)(.7)+(.03)(.3)=.014+.009=.023$

Hence the probability of a NONdefective is .977.

Let N stand for nondefective. The question here is $P(A|N)={P(AN)\over P(N)}$.

We have $P(N)=.977$ and from $.7=P(A)=P(AN)+P(AD)$

we can obtain $P(AN)$ since $P(AD)=(.02)(.7)$ from above.

I get .702149437 for the final answer, which seems reasonable since P(A)=.7 isn't far away.

4. is the answer 68.6% and if not can you expain the answer to me

and then what is the chance that is was produced by machine I